ADVANCED ELECTROMAGNETICS, Vol. 2, No. 1, February 2013 Novel antenna concepts via coordinate transformation Paul-Henri Tichit, Shah Nawaz Burokur, Xinying Wu, Dylan Germain, André de Lustrac * IEF, Univ. Paris-Sud, CNRS, UMR 8622, 91405 Orsay cedex, France *corresponding author, E-mail: andre.de-lustrac@u-psud.fr Abstract Coordinate transformation is an emerging field which offers a powerful and unprecedented ability to manipulate and control electromagnetic waves. Using this tool, we demonstrate the design of novel antenna concepts by tailoring their radiation properties. The wave manipulation is enabled through the use of engineered dispersive composite metamaterials that realize the space coordinate transformation. Three types of antennas are considered for design: a directive, a beam steerable and a quasi-isotropic one. Numerical simulations together with experimental measurements are performed in order to validate the coordinate transformation concept. Near-field cartography and far-field pattern measurements performed on a fabricated prototype agree qualitatively with Finite Element Method (FEM) simulations. It is shown that a particular radiation pattern can be tailored at ease into a desired one by modifying the electromagnetic properties of the space around radiator. This idea opens the way to novel antenna design techniques for various application domains such as the aeronautical and transport fields. 1. Introduction Coordinate transformation (also called transformation optics or transformation electromagnetics) is a powerful mathematical tool that is used to generate a new transformed space from an initial one where solutions of Maxwell’s equations are known by manipulating electromagnetic waves. As a first step, it consists in imagining a virtual space with desired topological properties, which will contain the underlying physics. This approach has been revived when J. B. Pendry et al. [1] have proposed an interpretation where permeability and permittivity tensors components can be viewed as a material in the original space. It is as if the new material mimicks the defined topological space. Since this pioneering work of J. B. Pendry and that of U. Leonhardt et al. [2], transformation optics is an emerging field where Maxwell’s equations are form invariant under a coordinate transformation. It offers an unconventional strategy to the design of novel class metamaterial devices. The most striking application conceived so far via coordinate transformation concept is the invisibility cloak for which various designs have been presented in microwave [3-5] and optical regimes [6-8]. Other interesting wave manipulation applications such as wave concentrators [9], field rotators [10], electromagnetic wormholes [11], waveguide transitions and bends [12-16] have also been proposed. Concerning antenna applications, focusing lens antennas [17-19] and the engineering of radiation patterns [20] have been proposed. The performances of an omnidirectional retroreflector [21] based on the transmutation of singularities [22] and Luneberg lenses [23] have also been experimentally demonstrated. An octave-bandwidth horn antenna has experimentally validated for satellite communications [24]. Recently, techniques of source transformation [25-27] have offered new opportunities for the design of active devices with source distribution included in the transformed space. Using this last approach, we review the design of three antenna models where the radiation pattern is tailored specifically in each case. The first one concerns an ultra- directive antenna obtained by stretching a source into an extended coherent radiator [28-30]. The design has been implemented through the use of judiciously engineered metamaterials and the device is shown experimentally to produce an ultra-directive emission. The idea has been extended to a second device, a wave bending one, so as to achieve a steered beam antenna via a rotational coordinate transformation. Experimental measurements have shown a beam steering as much as 66°. Finally, we present the numerical design of a quasi-isotropic antenna achieved by expanding the space around a directive source [31]. 2. Ultra-directive antenna The ultra-directive antenna is based on the transformation of a cylindrical space into a rectangular one. The schematic principle of the transformation is presented in Fig. 1. The theoretical underlying physics of the transformation involved here has been detailed recently in [28]. The concept is as follows: the imagined space of our proposed antenna is obtained by transforming a flat isotropic cylindrical half-space with zero Riemann curvature tensor described in polar coordinates {r, θ} into a flat space in squeezed Cartesian coordinates. x’, y’ and z’ are the coordinates in the virtual transformed rectangular space and x, y, z are those in the initial real cylindrical space. We assume free space in the cylinder, with isotropic permeability and permittivity tensors ε 0 and μ 0 . In the theoretical study of [28], we have shown that the coordinate transformation can be implemented by a material obeying the following tensors: